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June 2005 Up to equimorphism, hyperarithmetic is recursive
Antonio Montalbán
J. Symbolic Logic 70(2): 360-378 (June 2005). DOI: 10.2178/jsl/1120224717

Abstract

Two linear orderings are equimorphic if each can be embedded into the other. We prove that every hyperarithmetic linear ordering is equimorphic to a recursive one.

On the way to our main result we prove that a linear ordering has Hausdorff rank less than ω₁CK if and only if it is equimorphic to a recursive one. As a corollary of our proof we prove that, given a recursive ordinal α, the partial ordering of equimorphism types of linear orderings of Hausdorff rank at most α ordered by embeddablity is recursively presentable.

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Antonio Montalbán. "Up to equimorphism, hyperarithmetic is recursive." J. Symbolic Logic 70 (2) 360 - 378, June 2005. https://doi.org/10.2178/jsl/1120224717

Information

Published: June 2005
First available in Project Euclid: 1 July 2005

zbMATH: 1089.03036
MathSciNet: MR2140035
Digital Object Identifier: 10.2178/jsl/1120224717

Rights: Copyright © 2005 Association for Symbolic Logic

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Vol.70 • No. 2 • June 2005
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